Tunneling is one of the most well-known quantum effects and has been a long standing important subject of quantum mechanics. The simplest tunneling phenomenon is demonstrated by a square potential barrier wherein the Schrödinger equation predicts a non-zero probability that a particle initially on the far left of the barrier is transmitted to the far right even if its energy is less than the barrier height. However, tunneling becomes problematic when one associates the time it takes a wavepacket to traverse the classically forbidden region [1]}, [2]} because it is compounded with the quantum time problem (QTP), and superluminality. Standard quantum mechanics only treats time as a parameter, as such, the quantum tunneling time problem may be ill-defined because there is no canonical formalism in standard quantum mechanics to answer questions regarding time durations [3]}, [4]}. Moreover, a dynamical treatment of time, e.g., a time operator, has been met with pessimism because of Pauli's no-go theorem [5]} on the existence of a time operator. This has led to several definitions of tunneling time using a parametric approach, e.g. Wigner phase time [6]}, Büttiker-Landauer time [7]}, Larmor time [8]}, [9]}, [10]}, Pollak-Miller time [11]}, dwell time [12]}, among many others [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}. However, one of us has shown that Pauli's no-go theorem does not hold in the single Hilbert space formulation of quantum mechanics [23]} and constructed a corresponding barrier traversal time operator to calculate the tunneling time [15]}. By doing so, tunneling time was treated as a dynamical observable which addresses any contentions on tunneling time being an ill-defined problem.
